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Math Help - mean and standard deviation

  1. #1
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    mean and standard deviation

    I have scanned over and over a similar problem on the forum, i just cannot understand.
    I understand that i am to read the normal Z tables like a stem plot but cannot find any connection to the answers given.

    Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
    Mean- 1250 Std. dev = 120

    (a) Find Pr(X > 1250) This is the mean so prob has to equal half... (0.5)

    (b) Find Pr(1250 < X < 1380)
    = Find Z first z = 1380 1250 / 120 = 130/120 = 1.083
    Pr(1250 < X < 1380) = look up z in tables

    (c) Find Pr(1135 < X < 1275)
    = Find Z (you need 2 values lower should work out as -0.958 and upper as 0.208)tutor notes
    = Pr(1135 < X < 1275) = look up Z values in tables and add together
    It is spelled out for me, i cant see where to go. how to get the Z,
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  2. #2
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    Hello,

    Quote Originally Posted by roxy View Post
    I have scanned over and over a similar problem on the forum, i just cannot understand.
    I understand that i am to read the normal Z tables like a stem plot but cannot find any connection to the answers given.

    Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
    Mean- 1250 Std. dev = 120

    (a) Find Pr(X > 1250) This is the mean so prob has to equal half... (0.5)

    (b) Find Pr(1250 < X < 1380)
    = Find Z first z = 1380 – 1250 / 120 = 130/120 = 1.083
    Pr(1250 < X < 1380) = look up z in tables

    (c) Find Pr(1135 < X < 1275)
    = Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
    = Pr(1135 < X < 1275) = look up Z values in tables and add together
    It is spelled out for me, i cant see where to go. how to get the Z,
    The z-table is made up for a standard normal distribution..

    So for a random variable X that has a normal distribution, a mean of \mu and a standard dev of \sigma, there is Z that has a standard normal distribution :

    Z=\frac{X-\mu}{\sigma}

    So transform P(1250<X<1380)=P \left(\frac{1250-1250}{120}<Z<\frac{1380-1250}{120} \right) =P(0<Z<1.083)= \text{look on the table}


    Same for P(1135<X<1275)=P(-0.9583<Z<0.2083)=P(Z<0.2083) -P(-0.9583<Z) =P(Z<0.2083)-(1-P(Z<-0.9583))=P(Z<0.2083)+P(Z<-0.9583)-1
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  3. #3
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    Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation
    (c) Find Pr(1135 < X < 1275)
    = Find Z (you need 2 values lower should work out as -0.958 and upper as 0.208)tutor notes
    = Pr(1135 < X < 1275) = look up Z values in tables and add together
    It is spelled out for me, i cant see where to go. how to get the Z,[/quote]

    For this one fins the two z-score, then look them up to see what probability corresponds.

    z=\frac{x-{\mu}}{\sigma}

    -.958=\frac{1135-1250}{120}

    Look up in the table and we get .169

    .208=\frac{1275-1250}{120}

    Look up in the table and we get .582

    Subtract and we get a probability of .413
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  4. #4
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    Smile

    Thankyou, i will have a look at all the info you sent. sorry i cant give you chocolates, maybe virtual.
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  5. #5
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    still stuck



    Look up in the table and we get .169



    Look up in the table and we get .582

    Subtract and we get a probability of .413 _

    this .169 and .582 is where i am having trouble. when i look the .958 up in the z tables all i get is .3309 . when i look up z= .208 i find .824
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